Wednesday, October 2, 2013

From the denial of divine simplicity to atheism

Premises 1-3 of the following valid argument seem plausible:

  1. If God is not simple, then God is infinitely complex.
  2. If God is infinitely complex, then atheistic naturalism is a better theory than theism. (Ockham's Razor)
  3. If atheistic naturalism is a better theory than theism, then there is no God.
  4. So, if God is not simple, then there is no God.
So, theists should accept divine simplicity.


Heath White said...

I've never thought about this deeply, but... wouldn't a Trinity of *three* persons be a non-simple God? Obviously the answer here is supposed to be 'no' but I don't see how that answer is supposed to go.

Alexander R Pruss said...

This all too quick answer is that the persons aren't parts of God.

Drew said...

It seems that this will depend on one's definition of simplicity. I don't even know how to think of things like the baptism of Jesus, the cry of "My God my God, why have you forsaken me?" Jesus' prayers to the Father, or the statement "But concerning that day and hour no one knows, not even the angels of heaven, nor the Son, but the Father only" on divine simplicity.

These verses seem unintelligible apart from the hypothesis that the Son and the Father are two separate centers of self-consciousness. To say that they are not parts is to strip the term of all meaning.

Alexander R Pruss said...

If they are parts of God, they are proper parts of God. But a proper part is not the whole. So if the Father is a part of God, the Father is not God.

Aquinas' take is that there are two identity relations: numerical identity of essences and numerical identity of individuals. In ordinary cases, there is one essence per individual, and so the two relations are coextensive. But in the case of God, there is one essence per three individuals, and in the case of the incarnate Christ, there are two essences for a single individual.

Anonymous said...

What makes the first premise plausible? Isn't it logically possible (on the assumption that it's logically possible that God be complex) that God be composed of a finite number of (proper?) parts?

Also, I suppose a Theist like William Lane Craig, who denies divine simplicity, could simply argue that all things being equal you're right, but all things considered Naturalism is less plausible. Indeed, I could imagine somebody arguing that Naturalism, though simpler, just isn't a sufficient explanation at all, and thus we're stuck with 'complex' theism.

Also, what do you think about arguing as follows:

1. The more parsimonious theory of any two theories ought to be preferred, just in case both are possible.
2. Possibly, God is simple.
3. Possibly, God is complex.
4. The theory that God is simple is more parsimonious than the theory that God is complex.
5. Therefore, the theory that God is simple ought to be preferred.

Finally, to Heath White, I agree (With Dr. Pruss) that to call the persons of the trinity 'parts' of God is literally bad grammar.

Alexander R Pruss said...

It's perhaps epistemically possible, but is it plausible?

Suppose one is impressed with the complexity that minds must have, and that's one's reason for denying divine simplicity. Well, surely if one thinks minds need complexity, one will think that a more sophisticated mind will be more complex.

Or suppose one believes in substance-accident complexity in God: God has accidents. Well, presumably then God will have lots of accidents.


VeritasSeeker said...

Dr. Pruss,

Why is (1) true? Couldn't God be finitely complex if he is not simple?

Furthermore, what do you mean by "complex" and "simple"? Do you just mean to signify the presence and absence of metaphysical composition by the words? If so, then it seems like your premise can be rephrased as follows:

(1*) If it is not the case that God has no parts, then God has infinitely many parts.

But this is logically equivalent to the following:

(1**): If God has parts, then God has infinitely many parts.

I don't see any reason to think that (1**) is true.

Richard A. Christian said...

When considering competing theories one should take into account more than mere simplicity, and the theist who does not accept divine simplicity would say (and I think rightly) that theism has greater explanatory power despite God being complex. So (2) is a little rushed, you have to show that the simplicity of atheistic naturalism makes it the preferable theory despite theism without divine simplicity ( I’ll call theism plus the denial of divine simplicity ‘complex-theism’) being of greater explanatory power. One could reply that a thing such as a contingent universe entails the existence of a necessary being, or that there needs to be a greatest possible being given some ontological arguments, and so forth- and some of these deductive arguments don’t seem to go one way or another on God’s simplicity. So there are features of the world that entail theism whether simple-theism or complex-theism, but given those arguments it wouldn't follow that complex-theism implies that atheistic naturalism is the better theory.

Anonymous said...

I'm not sure I see the force of this argument. If you take, for example, properties to be proper parts of a thing, then God will have infinitely many proper parts, and if you think this is sufficient for his being infinitely complex, then he will be. Is this your idea?

But then *everything* is infinitely complex, since everything has an infinite number of proper parts by virtue of having an infinite number of properties (if x has F, then x has F or F*...).

So say the competing theory is something like Oppy's naturalism, where there's an 'initial naturalistic state' that is necessary. It too will be infinitely complex, on this view. So where's the problem?

Edgar Foster said...

I agree that simplicity and complexity need to be disambiguated a little more before the conclusion of the argument is granted. The doctrine of divine simplicity (simplicitas Dei) posits numerous ways in which God is supposed to be non-mereological. One familiar claim is that God has no temporal or spatial parts; he is simple in that sense (among other ways). But the timelessness of God is a very contentious issue although most would probably concede that deity is non-spatial. Many issues must also be worked out regarding time before the argument flies.

Alexander R Pruss said...


Yeah, if something like the ontological argument were to work for a complex God, then that would be a way out of 2.

As for the inference from contingency to a necessary being, I think the idea that the initial state of the universe is necessary compares well with the hypothesis of an infinitely complex God. Granted, one needs to give up on the modal intuition that the initial state could have been different. But the same kinds of reasons that lead one to think the initial state could have been different--the parts could have been differently arranged, etc.--also make it plausible that a complex God exists contingently.


Properties at least typically are not parts of the entity, though the particular tropes of the instantiation relation might be.

In any case, your argument presupposes an abundant theory of properties. And for complexity comparisons, we need shouldn't compare the number of properties a thing has, but the number of fundamental (or sparse) properties a thing has.

And I think it's plausible that if God has more than one fundamental property, he has infinitely many. But it seems reasonable to suppose the initial state of the world has only finitely many fundamental properties. Or if infinitely, there will be a cardinality bound, but it would be too weird to think that there would be any cardinality bound on the fundamental properties of an infinitely complex God.

Alexander R Pruss said...
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Alexander R Pruss said...

I think one thing that seriously weakens the argument is the thought that the same line of thought that leads to (1) also leads to the following theologically problematic and probably heretical conclusion:
(*) If God is more than one person, then God is infinitely many persons.

(I wrote "probably heretical", because at present I don't know any official Church statement that God is *only* three persons. However, the "only" claim is clearly implicit in the Christian Tradition, and hence is binding on faith.)

I think there may be a philosophically relevant difference between (1) and (*). Namely, there are some principled plausibilistic reasons given by thinkers like Aquinas as to why the number of processions in God is exactly two (and hence there are three persons, since each procession generates exactly one additional person).

On the other hand, the reasons for denying simplicity are two-fold. There are Trinity-based reasons. Those, I think, just don't work. They lead to a mistaken view of the Trinity on which the persons are proper parts of God, which does not make it possible to say of each person that he is God.

And there are philosophical reasons, based on the idea that different divine attributes (justice, mercy, etc.) need to have separate grounds in God, or the idea that a mind that has many ideas must be complex, and the like. These kinds of reasons suggest that an infinite being like God will have infinite complexity.

Scott said...

I thought the doctrine of Divine Simplicity required much more than the claim that God is simple in the sense that he doesn't have any parts. I thought the doctrine required that God was identical to each of His properties and that each of His properties was identical to each of His other properties. It seems like the Theist could hold that God is simple in one way without holding that God is simple in the Divine Simplicity way. So if simplicity means 'Divine Simplicity', then (1) would be false wouldn't it? And if simplicity means regular simplicity, then (4) doesn't get you to Divine Simplicity, it seems.

Alexander R Pruss said...

I think divine simplicity requires God to be identical with each of his constituents. The implications regarding divine properties depend on the details of the theory of properties.

Suppose one thinks that when an object x has a property P, then a metaphysical constituent of x is the token relation x's exemplifying of P. Then a consequence of divine simplicity will be that either God has only one property or that his exemplifying P1 is the same as his exemplifying P2. This could be true even if P1 is not identical with P2. Perhaps my exemplifying mammality is nothing different than my exemplifying humanity, even though humanity is not mammality.

Of course, then there is a further question whether God's exemplifying properties, where the properties are in a Platonic realm apart from God, is compatible with theism, given theism's commitment to the claim that everything distinct from God is created by God.

Edgar Foster said...


in my remarks, I did say that simplicity refers to God not having any spatiotemporal parts. However, I included the qualifier "among other things." You are correct that there's more to divine simplicity than no spatial or temporal parts. Aquinas contends that God has no potency and that essence and existence coincide in divina. So there's more to it than a lack of mereological relations. But I was just trying to sketch what divine simplicity might entail (prima facie).

Unknown said...

It seems that we have good reason to believe in an infinite hierarchy of mathematical, logical, and mereological entities. So suppose that it is metaphysically possible that this whole hierarchy, taken collectively, is the mind of God. Suppose moreover that, necessarily, this whole hierarchy is part of the mind of God. (I.e., it would have been the mind of God had God not created anything contingent. However, as things actually are, God's mind has other parts, too, as a result of His having created contingent things.)

It follows from these suppositions that necessarily, God's mind has infinitely many constituents. Even if we knew that theism entailed this result, would this result provide any reason to prefer naturalism to theism? I think that, at least, it would provide very little reason for that preference. A version of naturalism which lacked the infinite hierarchy of logic, math, and parthood would indeed be simpler in some sense than a version of theism which included that hierarchy. However, such a version of naturalism would be more implausible than that version of theism on the whole, because it is highly implausible that the hierarchy in question doesn't exist.

So even if God's mind is infinitely complex, theism is still more plausible than naturalism.

Alexander R Pruss said...


That's a very nice response, in that it shows how one might believe in complexity in God, but with the complexity no greater than that in a standard naturalism, since standard naturalism includes mathematics.

For the record, I think the apparent plurality of ideas in the mind of God doesn't give rise to complexity. In ourselves, a single mental state can ground knowledge of several claims. Thus, I know that I have two hands and that I have hands. This might be grounded in a single knowledge state.

Unknown said...


I personally tend to think that God has only one knowledge state --- (God's knowledge that P) = (God's knowledge that Q), even if P = Q. I think this works for God, but not for you and I, because God is mereologically maximal in a way we aren't. If I know that P, then typically, (the SOA that I know that P) is not itself part of my mind. Of course, it WOULD be a part of my mind IF, instead of just knowing that P, I also knew this SOA (the SOA that I know that P). So note that there's a chain here: I know that P; I know the SOA that I know that P; I know the SOA that I know the SOA that I know that P; etc. But since I can only know finitely many SOA's, eventually this chain tops out and we reach a point where I know something without knowing that I know it. (My knowing that last thing) is an SOA that is not part of my mind, so it is distinct from all the other, earlier SOA's, each of which is a part of my mind.

But God knows every SOA. So there is no topmost 'knowing' SOA of which God is the subject. So there is no 'God knows something' SOA which is not a part of God's mind. So, then, whereas in my case we can infer that not all my 'knowing' SOA's are identical (since some are parts of my mind and others are not), we cannot infer this in God's case.

This is, of course, a negative argument for the simplicity of God's knowledge states. A positive argument would instead go something like this: X itself is a part of each of X's knowing states. So God is a part of each of God's knowing states. But God knows each of God's knowing states, because God knows everything. If X knows Y, then Y is a part of X. So each of God's knowing states is a part of God. So God and each of God's knowing states are reciprocal parts (each is a part of the other). But parthood is anti-symmetric. Therefore, God is each of God's knowing states. Identity is (in this context) transitive. So each of God's knowing states is each of God's knowing states.

I think the same argument works for EVERY state of affairs of which God is a constituent. Therefore, all such states of affairs are identical to one another and to God.

While I accept all that, what I don't see is any strong argument to believe that God is MEREOLOGICALLY simple. I.e., even if His states of affairs are all identical, He might still have infinitely many distinct parts. In fact, since I take 'X knows P' to entail that P is a part of X (I even appealed to this premise in my argument that God's SOA's are all identical), and since I think there are infinitely many distinct propositions that God knows, it follows from my view that there are indeed infinitely many distinct things which are all parts of God. Even as a traditional Christian (I am one!), I see no reason why this view is problematic.

Alexander R Pruss said...

Everything that isn't God is created by God.
Thus, if God has any proper part, that part is created by God.
No being that has proper parts can be the creator of all of its proper parts.

Unknown said...

'No being that has proper parts can be the creator of all its proper parts' -- why?